At which point is a kick-off an appropriate restart?

A kick-off is an appropriate restart after a goal has been scored. This is standard practice in soccer, as the game is paused to allow the opposing team to restart play from the center of the field. When a goal is scored, the team that conceded the goal must kick off from the center spot, which provides a clear and defined method to resume play and allows the scoring team to celebrate or reset their defense.

The start of the first half also involves a kick-off, but it's important to note that the question focuses specifically on the instances relevant to the choices provided. While a kick-off does occur at the beginning of the match, the correct answer as it relates to the specific context of restart situations after a notable play is after a goal.

In contrast, a throw-in and the end of the game do not involve a kick-off. A throw-in is a method to restart play after the ball has gone out of bounds on the sides of the field. At the end of the game, the match concludes and no further restarts occur. Hence, the choice related to after a goal is the only one that aligns with the rules regarding when a kick-off must take place.